Answer :

[tex]f(x) = 2x - 6 \\\\ ff^{-1}(x) = 2f^{-1}(x) - 6 \\\\ x = 2f^{-1}(x) - 6 \\\\ \implies f^{-1}(x) = \frac{x + 6}{2} \\\\\\ f^{-1}(2) = \frac{2 + 6}{2 } = \frac{8}{2} = \boxed{4}[/tex]